To decapitate him they'd need something that could cut through adamantium though.

Not necessarily. You'd just had to be able to make a clean cut through the cartilage that connects his vertibrae. That's actually something the comics always got wrong, when it depicted larger stronger characters trying to rip Wolverine apart. His bones can't break, but the connective tissue holding them together sure would. Ultimate Wolverine vs Hulk actually got that instance right.

Now, if they added something saying that they also interwove very smalls strands of adamantium with his connective tissue, then yeah, he wouldn't be able to get ripped apart/cut apart or any thing like that.